Solve for $x$ and $y$ using elimination. ${5x-3y = 5}$ ${6x-3y = 12}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-1$ ${-5x+3y = -5}$ $6x-3y = 12$ Add the top and bottom equations together. ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {5x-3y = 5}\thinspace$ to find $y$ ${5}{(7)}{ - 3y = 5}$ $35-3y = 5$ $35{-35} - 3y = 5{-35}$ $-3y = -30$ $\dfrac{-3y}{{-3}} = \dfrac{-30}{{-3}}$ ${y = 10}$ You can also plug ${x = 7}$ into $\thinspace {6x-3y = 12}\thinspace$ and get the same answer for $y$ : ${6}{(7)}{ - 3y = 12}$ ${y = 10}$